1. Section 1.7 Using Variables and Formulas

2. 1.7 Lecture Guide: Using Variables and Formulas Objective 1: Evaluate an algebraic expression for specific values of the variables. Evaluate for each value of x. (Hint: See Technology Perspective 1.7.1 for using a calculator or a spreadsheet to check your work.) 1.2.3.

3. Evaluate the following expressions for and. 4.5.6.

4. Evaluate the following expressions for and. 7.8.

5. Algebraic formulas are used in nearly all areas of mathematics, business, and the sciences. A formula describes a relationship between specific variables. For example, the area A of a triangle is given by the formula, where b represents the length of the base of the triangle and h represents the height of the triangle. This relationship holds true for all triangles. Objective 2: Use algebraic formulas.

6. Find the area of each triangle. Remember, this area is given in square units. A = ______ 9. 4 cm 7 cm

7. A = ______10. 3 in 8 in Find the area of each triangle. Remember, this area is given in square units.

8. The formula for Fahrenheit temperature is given by 11.. Find the Fahrenheit temperature if the Celsius temperature C is.

9. 12. The formula for the amount in a bank account paying a simple interest rate R for T years is given by, where P is the principal or initial amount. Find the amount in a bank account after 1 year if there was an initial deposit of $5,000 and the account earned 5% simple interest.

10. 13. The formula for the perimeter of a rectangle is given by. Find the perimeter P of a rectangle if the length l is 20 meters and the width w is 35 meters.

11. One common usage of subscript notation is the slope formula,, which will be developed in Chapter 3. This formula is used to calculate m, the slope of a line that passes through the points and. Objective 3: Use subscript notation.

12. and. 14.Use this formula to calculate the value of m for the line through the points

13. and. 15.Use this formula to calculate the value of m for the line through the points

14. A sequence is an ordered set of numbers with a first number, a second number, a third number, etc. Subscript notation often is used to denote the terms of a sequence: These terms are read a sub one, a sub two, and a sub n, respectively. If a sequence follows a predictable pattern, then we may be able to describe this pattern with a formula for. Consider the sequence 5, 4, 3, 2. Here

15. Use each formula to calculate the first three terms of each sequence. 16.

16. Use each formula to calculate the first three terms of each sequence. 17.

17. Objective 4: Check a possible solution of an equation. A solution of an equation is a value for the variable that satisfies the equation. This means that when the value is substituted for the variable, the expressions on each side of the equation will have the ____________ value.

18. Check whether each indicated value of x is a solution of the given equation. 18. (a) Check (b) Check

19. Check whether each indicated value of x is a solution of the given equation. 19. (a) Check (b) Check

20. 20. (a) Check (b) Check Check whether each indicated value of x is a solution of the given equation.

21. 21. (a) Check (b) Check Check whether each indicated value of x is a solution of the given equation.